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Stephen Hawking was once told by an editor that every equation in
a book would halve the sales. Curiously, the opposite seems to happen when it comes to research
papers. Include a bit of maths in the abstract (a kind of summary) and people rate your paper higher —
even if the maths makes no sense at all. At least this is what a
study
published in the Journal Judgment
and decision making seems to suggests.

Maths: incomprehensible but impressive?

Kimmo Eriksson, the author of the study, took two abstracts from
papers published in respected research journals. One
paper was in evolutionary anthropology and the other in sociology. He
gave these two abstracts to 200 people, all experienced in
reading research papers and all with a postgraduate degree, and asked
them to rate the quality of the research described in the
abstracts. What the 200 participants didn't know is that Eriksson had
randomly added a bit of maths to one of the
two abstracts they were looking at. It came in the shape of the following sentence, taken
from a third and unrelated paper:

A mathematical model is developed to describe sequential effects.

That sentence made absolutely no sense in either context.

People
with degrees in maths, science and technology weren't fooled by the
fake maths, but those with degrees in other areas, such as
the humanities, social sciences and education, were: they rated the
abstract with the tacked-on sentence higher. "The
experimental results suggest a bias for nonsense maths in judgements
of quality of research," says Eriksson in his paper.

The effect is probably down to a basic feature of human nature: we
tend to be in awe of things we feel we can't understand. Maths, with its
reassuring ring of objectivity and definiteness, can boost the
credibility of research results. This can be perfectly legitimate: maths is
a useful tool in many areas outside of hard science. But Eriksson,
who moved from pure maths to interdisciplinary work in social
science and cultural studies, isn't entirely happy with the way it is
being used in these fields. "In areas like sociology or evolutionary
anthropology I found mathematics often to be used in ways that from my
viewpoint were illegitimate, such as to make a point that would better
be made with only simple logic, or to uncritically take properties of
a mathematical model to be properties of the real world, or to include
mathematics to make a paper look more impressive," he says in his
paper. "If mathematics is held in awe in an unhealthy way, its use is not subjected to sufficient levels of critical thinking."

You can read Eriksson's paper here. There is also an interesting article on this and other bogus maths effect in this article in the Wall Street Journal.